"money unit" is a correct and usable phrase in written English.
You can use it as a general way to refer to a unit of currency, either in a particular country or globally. For example, you could say: "The exchange rate for the US money unit is currently one to two."
Would Use Power as Money Unit.
Notes on the establisment of a money unit, and of a coinage for the United States.
The present paper presents a further development casting the definition into dimensionless quantities that make the index get a pure unit of time and not the somewhat obscure unit as a power product of a money unit and a time unit.
The consequence … is to degrade the money unit; obliging creditors to receive less than their just dues -- and depreciating property of every kind….
The components of the jth column of Φ describe how each money unit, say each dollar, of consumer payments for the product of sector j is ultimately distributed among the owners of the k factors.
Many trade models explain trade measured in money units.
The downside of this is that we cannot easily link the model to economic statistics of trade in money units.
Two players, A and B, have to agree on the division of 10 money units, in this case Swiss francs.
This is then followed by a conversion step to go from money units to tonnes (needed because subsequent sub-models, such as modal spit, are in tonnes).
In each round, the three group members earned 0.5 money units for each token contributed to the project, regardless of the individual contribution.
Input-output tables describe, in money units, what each sector of the economy (e.g. textile manufacturing) delivers to the other sectors, also including the final demand by consumers, import and export.
